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Published in:
An Inaccessible Graph Read chapter Read first chapter

2011 | OriginalPaper | Chapter

Stochastically Incomplete Manifolds and Graphs

Author : Radosław Krzysztof Wojciechowski

Published in: Random Walks, Boundaries and Spectra

Publisher: Springer Basel

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We survey geometric properties which imply the stochastic incompleteness of the minimal diffusion process associated to the Laplacian on manifolds and graphs. In particular, we completely characterize stochastic incompleteness for spherically symmetric graphs and show that, in contrast to the case of Riemannian manifolds, there exist examples of stochastically incomplete graphs of polynomial volume growth.

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previous chapter Brownian Motion and Negative Curvature
next chapter Generalized Solutions and Spectrum for Dirichlet Forms on Graphs
Metadata
Title
Stochastically Incomplete Manifolds and Graphs
Author
Radosław Krzysztof Wojciechowski
Copyright Year
2011
Publisher
Springer Basel
Book
Random Walks, Boundaries and Spectra

Print ISBN: 978-3-0346-0243-3

Electronic ISBN: 978-3-0346-0244-0

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-3-0346-0244-0_9